library(tidyverse) # data manipulation
library(ggpubr) # producing data exploratory plots
library(modelsummary) # descriptive data
library(glmmTMB) # running generalised mixed models
library(DHARMa) # model diagnostics
library(performance) # model diagnostics
library(ggeffects) # partial effect plots
library(car) # running Anova on model
library(emmeans) # post-hoc analysisdf_adults_cleaned <- df_adults |>
mutate(FISH_ID = factor(FISH_ID),
Sex = factor(Sex),
Population = factor(Population),
Tank = factor(Tank),
Chamber = factor(Chamber),
System =factor(System),
Temperature =factor(Temperature),
True_resting=factor(True_resting))
df_males <- df_adults_cleaned |>
filter(Sex == "M")
df_females <- df_adults_cleaned |>
filter(Sex == "F")
df_adults_cleaned2 <- df_males |>
full_join(select(df_females, c("Tank","Temperature","Mass","Resting","Max","AAS","FISH_ID","Sex")), by="Tank") |>
mutate(Temperature.x = coalesce(Temperature.x, Temperature.y),
FISH_ID.x = coalesce(FISH_ID.x, FISH_ID.y),
Sex.x = coalesce(Sex.x, Sex.y),
Resting.midpoint = (Resting.x+Resting.y)/2,
Max.midpoint = (Max.x+Max.y)/2,
AAS.midpoint = (AAS.x+AAS.y)/2) df_jresp$Population <- fct_collapse(df_jresp$Population,
`Vlassof cay`= c("Vlassof reef", "Vlassof", "Vlassof Cay", "Vlassof cay"),
`Arlington reef` = c("Arlington reef","Arlginton reef"))
#df_jresp$Female <- fct_collapse(df_jresp$Female,
#`CARL359`= c("CARL359", "CARL59"))
df_jresp2 <- df_jresp |>
unite("F0", c("Male","Female"), sep="_", remove=FALSE) |>
mutate(across(1:7, factor),
Temperature = factor(Temperature),
True_resting = factor(True_resting))
#df_jresp2_rest <- df_jresp2 |>
#filter(True_resting == "Y")temp2a <- temp1a |>
left_join(select(df_adults_cleaned2, c("FISH_ID.x",
"Sex.x",
"Resting.x",
"Max.x",
"AAS.x",
"Mass.x")),
by="FISH_ID.x")temp2b <- temp1b |>
left_join(select(df_adults_cleaned2, c("FISH_ID.y",
"Sex.y",
"Resting.y",
"Max.y",
"AAS.y",
"Mass.y")),
by="FISH_ID.y") df_merged <- temp2a |>
left_join(select(temp2b, c("Clutch","Replicate",
"FISH_ID.y",
"Resting.y",
"Max.y",
"AAS.y",
"Mass.y")),
by=c("Clutch","Replicate"))df <- df_merged |>
mutate(Resting_MALE =Resting.x,
Max_MALE =Max.x,
AAS_MALE =AAS.x,
Mass_MALE =Mass.x,
FISH_ID.y =FISH_ID.x,#makes more sense for males to be .y instead of .x
FISH_ID.x =FISH_ID.x,
Resting_FEMALE =Resting.y,
Max_FEMALE =Max.y,
AAS_FEMALE =AAS.y,
Mass_FEMALE =Mass.y) |>
mutate(Resting_MALE = Resting_MALE/Mass_MALE,
Resting_FEMALE =Resting_FEMALE/Mass_FEMALE) |>
mutate(Resting_MID =(Resting_MALE+Resting_FEMALE)/2) |> # easier to do it again
filter(True_resting == "Y") |> # this should remove 10 individuals from the df
mutate(Resting_MID =coalesce(Resting_MID, Resting_MALE)) |>
mutate(Resting_MID =coalesce(Resting_MID, Resting_FEMALE)) |>
drop_na(Resting) |>
group_by(Clutch) |>
mutate(MEDIAN_Resting =median(Resting_kg_wet)) |>
ungroup() |>
select(-c(Replicate, Chamber, System, Volume, Date_tested, Swim, Mass, Dry_mass, 18:26)) |>
distinct() |>
drop_na(Resting_MID)plot2 <- ggplot(df, aes(x=Resting_MALE, y=MEDIAN_Resting, color=Temperature)) +
stat_smooth(method = "lm") +
#geom_point(alpha=0.1) +
ggtitle("Offspring-male relationship") +
xlab("Resting (offspring)") +
ylab("Resting (parental-male)") +
theme_classic() +
theme(legend.position = "bottom")
plot2plot <- ggplot(df, aes(x=Resting_MID, y=MEDIAN_Resting, color=Temperature)) +
stat_smooth(method = "lm") +
#geom_point(alpha=0.1) +
ggtitle("Offspring-midpoint relationship") +
xlab("Resting (offspring)") + ylab("Resting (parental-midpoint)") +
theme_classic() +
theme(legend.position = 'right')
plot| Population | 27 | 28.5 | 30 |
|---|---|---|---|
| Arlington reef | 7 | 6 | 3 |
| Pretty patches | 4 | 3 | 5 |
| Sudbury reef | 4 | 2 | 2 |
| Vlassof cay | 4 | 0 | 4 |
| F0 | 27 | 28.5 | 30 |
|---|---|---|---|
| CARL217_CARL226 | 0 | 1 | 0 |
| CARL218_CARL222 | 0 | 0 | 2 |
| CARL230_CARL235 | 0 | 0 | 0 |
| CARL233_CARL215 | 0 | 0 | 0 |
| CARL237_CARL219 | 2 | 0 | 0 |
| CARL241_CARL239 | 2 | 0 | 0 |
| CARL249_CARL360 | 0 | 0 | 1 |
| CARL335_CARL359 | 0 | 2 | 0 |
| CARL338_CARL345 | 0 | 1 | 0 |
| CARL344_CARL370 | 0 | 0 | 0 |
| CARL354_CARL355 | 3 | 0 | 0 |
| CARL360_CARL249 | 0 | 0 | 0 |
| CARL367_CARL363 | 0 | 1 | 0 |
| CARL369_CARL349 | 0 | 1 | 0 |
| CPRE189_CPRE202 | 0 | 0 | 2 |
| CPRE372_CPRE209 | 1 | 0 | 0 |
| CPRE372_CPRE370 | 1 | 0 | 0 |
| CPRE375_CPRE377 | 2 | 0 | 0 |
| CPRE391_CPRE390 | 0 | 0 | 1 |
| CPRE447_CPRE452 | 0 | 0 | 2 |
| CPRE453_CPRE459 | 0 | 1 | 0 |
| CPRE521_CPRE524 | 0 | 1 | 0 |
| CPRE550_CPRE533 | 0 | 1 | 0 |
| CSUD002_CSUD213 | 0 | 1 | 0 |
| CSUD009_CSUD212 | 2 | 0 | 0 |
| CSUD013_CSUD017 | 2 | 0 | 0 |
| CSUD016_CSUD078 | 0 | 1 | 0 |
| CSUD312_CSUD304 | 0 | 0 | 2 |
| CVLA049_CVLA098 | 0 | 0 | 0 |
| CVLA089_CVLA059 | 0 | 0 | 1 |
| CVLA102_CVLA466 | 1 | 0 | 0 |
| CVLA106_CVLA091 | 0 | 0 | 2 |
| CVLA468_CVLA477 | 2 | 0 | 0 |
| CVLA486_CVLA463 | 1 | 0 | 0 |
| CVLA498_CVLA493 | 0 | 0 | 1 |
| Temperature | NUnique | mean | median | min | max | sd | Histogram |
|---|---|---|---|---|---|---|---|
| 27 | 9 | 6.57 | 6.14 | 4.18 | 10.09 | 1.82 | ▅▂▃▇▃▇▂ |
| 28.5 | 10 | 6.07 | 5.71 | 4.40 | 8.49 | 1.40 | ▇▂▂▅▂▅▂ |
| 30 | 6 | 6.73 | 6.18 | 5.14 | 9.15 | 1.46 | ▅▂▇▅▅ |
| Population | 27 | 28.5 | 30 |
|---|---|---|---|
| Arlington reef | 8 | 7 | 4 |
| Pretty patches | 4 | 6 | 4 |
| Sudbury reef | 4 | 3 | 2 |
| Vlassof cay | 6 | 2 | 5 |
datasummary(Factor(Population) ~ Factor(Temperature)*Factor(Sex),
data = df_adults_cleaned,
fmt = "%.0f")| 27 | 28.5 | 30 | ||||
|---|---|---|---|---|---|---|
| Population | F | M | F | M | F | M |
| Arlington reef | 4 | 4 | 2 | 5 | 2 | 2 |
| Pretty patches | 2 | 2 | 3 | 3 | 3 | 1 |
| Sudbury reef | 2 | 2 | 1 | 2 | 1 | 1 |
| Vlassof cay | 3 | 3 | 1 | 1 | 3 | 2 |
Pairs
datasummary(Factor(Population)*Factor(Temperature.x) ~ AAS.midpoint*(NUnique),
data = df_adults_cleaned2,
fmt = "%.0f")| Population | Temperature.x | NUnique |
|---|---|---|
| Arlington reef | 27 | 3 |
| 28.5 | 2 | |
| 30 | 1 | |
| Pretty patches | 27 | 2 |
| 28.5 | 3 | |
| 30 | 1 | |
| Sudbury reef | 27 | 2 |
| 28.5 | 2 | |
| 30 | 1 | |
| Vlassof cay | 27 | 3 |
| 28.5 | 1 | |
| 30 | 2 |
| Temperature | NUnique | mean | median | min | max | sd | Histogram |
|---|---|---|---|---|---|---|---|
| 27 | 19 | 6.36 | 6.14 | 3.82 | 10.09 | 1.67 | ▃▃▅▇▃▃▂▂▂▂ |
| 28.5 | 16 | 6.29 | 6.23 | 4.35 | 8.49 | 1.41 | ▇▂▅▂▃▃▃▂ |
| 30 | 14 | 7.17 | 6.86 | 5.14 | 9.15 | 1.43 | ▅▂▇▂▂▂▇▅ |
After figuring out which random factors will be incorporated into the model we will start to examine out fixed factors. Some fixed factors such as Resting_(FE)MALE and TEMPERATURE will be essential to answering questions we have around heritability. Another factor that will be included is Dry_mass - which it should be pointed out in this experiment refers to the mass of fish after they were blotted dry with paper towel rather than completely dried out. Larger fish consume more oxygen, therefore, we need to account for this known relationship within our model. Out model will look something like this:
If we had alternative hypotheses to test would would do so at this stage. But in this instance the experiment was designed to answer a specific question via limiting potential covariates.
Great now lets check how out model performed via model validation techniques
To check out model performance we will be using two different packages that perform model diagnositics. The packages used here are just examples, there are other packages out there that can provide the same function.
## Object of Class DHARMa with simulated residuals based on 250 simulations with refit = FALSE . See ?DHARMa::simulateResiduals for help.
##
## Scaled residual values: 0.056 0.04 0.28 0.212 0.788 0.184 0.188 0.956 0.708 0.156 0.188 0.376 0.712 0.936 0.968 0.572 0.8 0.66 0.852 0.18 ...
## $uniformity
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: simulationOutput$scaledResiduals
## D = 0.12211, p-value = 0.6226
## alternative hypothesis: two-sided
##
##
## $dispersion
##
## DHARMa nonparametric dispersion test via sd of residuals fitted vs.
## simulated
##
## data: simulationOutput
## dispersion = 1.0253, p-value = 0.84
## alternative hypothesis: two.sided
##
##
## $outliers
##
## DHARMa outlier test based on exact binomial test with approximate
## expectations
##
## data: simulationOutput
## outliers at both margin(s) = 0, observations = 38, p-value = 1
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
## 0.00000000 0.09251276
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 )
## 0
## $uniformity
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: simulationOutput$scaledResiduals
## D = 0.12211, p-value = 0.6226
## alternative hypothesis: two-sided
##
##
## $dispersion
##
## DHARMa nonparametric dispersion test via sd of residuals fitted vs.
## simulated
##
## data: simulationOutput
## dispersion = 1.0253, p-value = 0.84
## alternative hypothesis: two.sided
##
##
## $outliers
##
## DHARMa outlier test based on exact binomial test with approximate
## expectations
##
## data: simulationOutput
## outliers at both margin(s) = 0, observations = 38, p-value = 1
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
## 0.00000000 0.09251276
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 )
## 0
## Family: gaussian ( identity )
## Formula: MEDIAN_Resting ~ scale(Resting_MALE) * Temperature
## Data: df
##
## AIC BIC logLik deviance df.resid
## 410.5 421.9 -198.2 396.5 31
##
##
## Dispersion estimate for gaussian family (sigma^2): 1.99e+03
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 360.658 13.508 26.699 < 2e-16 ***
## scale(Resting_MALE) 14.569 15.140 0.962 0.33591
## Temperature28.5 37.527 19.191 1.955 0.05053 .
## Temperature30 67.010 22.087 3.034 0.00241 **
## scale(Resting_MALE):Temperature28.5 -6.427 23.361 -0.275 0.78324
## scale(Resting_MALE):Temperature30 -35.345 20.218 -1.748 0.08042 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 2.5 % 97.5 % Estimate
## (Intercept) 334.18265949 387.133802 360.658231
## scale(Resting_MALE) -15.10465354 44.242130 14.568738
## Temperature28.5 -0.08588536 75.139531 37.526823
## Temperature30 23.71964274 110.300830 67.010237
## scale(Resting_MALE):Temperature28.5 -52.21242315 39.359227 -6.426598
## scale(Resting_MALE):Temperature30 -74.97119345 4.280644 -35.345275
model1.1 |> emmeans(pairwise ~ Temperature, type="response") |>
summary(by=NULL, adjust="sidak", infer=TRUE)## NOTE: Results may be misleading due to involvement in interactions
## $emmeans
## Temperature emmean SE df lower.CL upper.CL t.ratio p.value
## 27 361 13.5 31 327 395 26.699 <.0001
## 28.5 398 13.6 31 364 433 29.212 <.0001
## 30 428 17.5 31 384 472 24.473 <.0001
##
## Confidence level used: 0.95
## Conf-level adjustment: sidak method for 3 estimates
## P value adjustment: sidak method for 3 tests
##
## $contrasts
## contrast estimate SE df lower.CL upper.CL t.ratio
## Temperature27 - Temperature28.5 -37.5 19.2 31 -86.0 10.9 -1.955
## Temperature27 - Temperature30 -67.0 22.1 31 -122.8 -11.3 -3.034
## Temperature28.5 - Temperature30 -29.5 22.2 31 -85.4 26.4 -1.330
## p.value
## 0.1683
## 0.0145
## 0.4747
##
## Confidence level used: 0.95
## Conf-level adjustment: sidak method for 3 estimates
## P value adjustment: sidak method for 3 tests
om.rest <- emmeans(model1.1, ~Resting_MALE*Temperature,
at =list(Resting_MALE =seq(from=106, to =241, by=1)))
om.rest.df <- as.data.frame(om.rest)
om.rest.obs <- drop_na(df, Resting_MALE, MEDIAN_Resting) |>
mutate(Pred =predict(model1.1, re.form =NA, type='response'),
Resid =residuals(model1.1, type ="response"),
Fit =Pred + Resid)
om.rest.obs.summarize <- om.rest.obs |>
group_by(Clutch, Temperature) |>
summarise(mean.rest =mean(Fit, na.rm=TRUE),
mean.rest_male =mean(Resting_MALE, na.rm=TRUE),
sd.rest =sd(Fit, na.rm =TRUE),
n.rest = n()) |>
mutate(se.rest = sd.rest / sqrt(n.rest),
lower.ci.rest =mean.rest - qt(1 - (0.05/2), n.rest -1) * se.rest,
upper.ci.rest =mean.rest + qt(1 - (0.05/2), n.rest - 1) * se.rest)|>
ungroup()## `summarise()` has grouped output by 'Clutch'. You can override using the
## `.groups` argument.
## Warning: There were 76 warnings in `mutate()`.
## The first warning was:
## ℹ In argument: `lower.ci.rest = mean.rest - qt(1 - (0.05/2), n.rest - 1) *
## se.rest`.
## ℹ In group 1: `Clutch = 38`.
## Caused by warning in `qt()`:
## ! NaNs produced
## ℹ Run `dplyr::last_dplyr_warnings()` to see the 75 remaining warnings.
ggplot(data =om.rest.df, aes(y=emmean, x=Resting_MALE)) +
stat_smooth(aes(color=Temperature),
method = "lm") +
geom_pointrange(data = om.rest.obs.summarize, aes(y =mean.rest, x=mean.rest_male,
ymin =lower.ci.rest,
ymax =upper.ci.rest, color = Temperature),
alpha =0.2) +
facet_wrap(~Temperature) +
theme_classic() +
theme(legend.position ="bottom")## `geom_smooth()` using formula = 'y ~ x'
## Warning: Removed 17 rows containing missing values or values outside the scale range
## (`geom_segment()`).
## Warning: Removed 11 rows containing missing values or values outside the scale range
## (`geom_segment()`).
## Warning: Removed 10 rows containing missing values or values outside the scale range
## (`geom_segment()`).
mid_model1.1 <- glmmTMB(MEDIAN_Resting ~ scale(Resting_MID)*Temperature,
family="gaussian",
data=df)Great now lets check how out model performed via model validation techniques
To check out model performance we will be using two different packages that perform model diagnositics. The packages used here are just examples, there are other packages out there that can provide the same function.
## Object of Class DHARMa with simulated residuals based on 250 simulations with refit = FALSE . See ?DHARMa::simulateResiduals for help.
##
## Scaled residual values: 0.036 0.504 0.056 0.212 0.34 0.064 0.704 0.172 0.232 0.196 0.952 0.704 0.308 0.164 0.364 0.812 0.928 0.792 0.524 0.968 ...
## $uniformity
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: simulationOutput$scaledResiduals
## D = 0.11309, p-value = 0.6269
## alternative hypothesis: two-sided
##
##
## $dispersion
##
## DHARMa nonparametric dispersion test via sd of residuals fitted vs.
## simulated
##
## data: simulationOutput
## dispersion = 1.0226, p-value = 0.808
## alternative hypothesis: two.sided
##
##
## $outliers
##
## DHARMa outlier test based on exact binomial test with approximate
## expectations
##
## data: simulationOutput
## outliers at both margin(s) = 0, observations = 44, p-value = 1
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
## 0.00000000 0.08041994
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 )
## 0
## $uniformity
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: simulationOutput$scaledResiduals
## D = 0.11309, p-value = 0.6269
## alternative hypothesis: two-sided
##
##
## $dispersion
##
## DHARMa nonparametric dispersion test via sd of residuals fitted vs.
## simulated
##
## data: simulationOutput
## dispersion = 1.0226, p-value = 0.808
## alternative hypothesis: two.sided
##
##
## $outliers
##
## DHARMa outlier test based on exact binomial test with approximate
## expectations
##
## data: simulationOutput
## outliers at both margin(s) = 0, observations = 44, p-value = 1
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
## 0.00000000 0.08041994
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 )
## 0
## Family: gaussian ( identity )
## Formula: MEDIAN_Resting ~ scale(Resting_MID) * Temperature
## Data: df
##
## AIC BIC logLik deviance df.resid
## 473.7 486.2 -229.8 459.7 37
##
##
## Dispersion estimate for gaussian family (sigma^2): 2.02e+03
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 354.8089 15.8638 22.366 <2e-16 ***
## scale(Resting_MID) 2.5967 16.8130 0.154 0.8773
## Temperature28.5 42.7136 20.9443 2.039 0.0414 *
## Temperature30 52.3823 24.1355 2.170 0.0300 *
## scale(Resting_MID):Temperature28.5 13.2855 24.5443 0.541 0.5883
## scale(Resting_MID):Temperature30 -0.5295 22.7682 -0.023 0.9814
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 2.5 % 97.5 % Estimate
## (Intercept) 323.716338 385.90140 354.8088679
## scale(Resting_MID) -30.356162 35.54963 2.5967353
## Temperature28.5 1.663573 83.76364 42.7136077
## Temperature30 5.077517 99.68706 52.3822901
## scale(Resting_MID):Temperature28.5 -34.820367 61.39137 13.2855020
## scale(Resting_MID):Temperature30 -45.154296 44.09532 -0.5294903
om.rest <- emmeans(mid_model1.1, ~Resting_MID*Temperature,
at =list(Resting_MID =seq(from=100, to =260, by=1)))
om.rest.df <- as.data.frame(om.rest)
om.rest.obs <- drop_na(df, Resting_MID, MEDIAN_Resting) |>
mutate(Pred =predict(mid_model1.1, re.form =NA, type='response'),
Resid =residuals(mid_model1.1, type ="response"),
Fit =Pred + Resid)
om.rest.obs.summarize <- om.rest.obs |>
group_by(Clutch, Temperature) |>
summarise(mean.rest =mean(Fit, na.rm=TRUE),
mean.rest_female =mean(Resting_MID, na.rm=TRUE),
sd.rest =sd(Fit, na.rm =TRUE),
n.rest = n()) |>
mutate(se.rest = sd.rest / sqrt(n.rest),
lower.ci.rest =mean.rest - qt(1 - (0.05/2), n.rest -1) * se.rest,
upper.ci.rest =mean.rest + qt(1 - (0.05/2), n.rest - 1) * se.rest)|>
ungroup()## `summarise()` has grouped output by 'Clutch'. You can override using the
## `.groups` argument.
## Warning: There were 88 warnings in `mutate()`.
## The first warning was:
## ℹ In argument: `lower.ci.rest = mean.rest - qt(1 - (0.05/2), n.rest - 1) *
## se.rest`.
## ℹ In group 1: `Clutch = 38`.
## Caused by warning in `qt()`:
## ! NaNs produced
## ℹ Run `dplyr::last_dplyr_warnings()` to see the 87 remaining warnings.
ggplot(data =om.rest.df, aes(y=emmean, x=Resting_MID)) +
stat_smooth(aes(color=Temperature),
method = "lm") +
geom_pointrange(data = om.rest.obs.summarize, aes(y =mean.rest, x=mean.rest_female,
ymin =lower.ci.rest,
ymax =upper.ci.rest, color = Temperature),
alpha =0.2) +
facet_wrap(~Temperature) +
theme_classic() +
theme(legend.position ="bottom")## `geom_smooth()` using formula = 'y ~ x'
## Warning: Removed 19 rows containing missing values or values outside the scale range
## (`geom_segment()`).
## Warning: Removed 11 rows containing missing values or values outside the scale range
## (`geom_segment()`).
## Warning: Removed 14 rows containing missing values or values outside the scale range
## (`geom_segment()`).